Question: $89$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $40$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Solution: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 89}$ ${x = 2y-40}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-40}$ for $x$ in the first equation. ${(2y-40)}{+ y = 89}$ Simplify and solve for $y$ $ 2y-40 + y = 89 $ $ 3y-40 = 89 $ $ 3y = 129 $ $ y = \dfrac{129}{3} $ ${y = 43}$ Now that you know ${y = 43}$ , plug it back into ${x = 2y-40}$ to find $x$ ${x = 2}{(43)}{ - 40}$ $x = 86 - 40$ ${x = 46}$ You can also plug ${y = 43}$ into ${x+y = 89}$ and get the same answer for $x$ ${x + }{(43)}{= 89}$ ${x = 46}$ There were $46$ home team fans and $43$ away team fans.